Which deform modifier, if any, would do this?
There is more of an indirect approach using the curve deform modifier.

Suppose I want o apply it a jagged circular line,I don't model it as a circular line,I model it as a normal line then deform it on a circle to become circular.

Here is the original object:

 


Select the circle(curve) and the object as the circle the active.
Press Ctrl+P then Curve deform
Now you have the circular shape (you can make it taller to completely fit).




To the main answer of the question:

All you have to do is changing the tilt of the curve.



Note:If the rotation of the object is nor deformed right,you have yo change the axis of deformation from the curve deform modifier.